At a certain point in the reentry of the space shuttle into the earth’s atmosphere, the...

At a certain point in the reentry of the space shuttle into the earth’s atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.66 m/s² at this altitude. The second component equals 12.90 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 48.2 km and has reduced its orbital velocity of 28 300 km/h to 15 450 km/h in the direction θ = 150^o. For this instant, calculate the radius of curvature ρ of the path and the rate at which the speed is changing.